About: Bit-reversal permutation

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In applied mathematics, a bit-reversal permutation is a permutation of a sequence of items, where is a power of two. It is defined by indexing the elements of the sequence by the numbers from to , representing each of these numbers by its binary representation (padded to have length exactly ), and mapping each item to the item whose representation has the same bits in the reversed order. Repeating the same permutation twice returns to the original ordering on the items, so the bit reversal permutation is an involution.

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rdf:type	yago:WikicatCombinatorialAlgorithms yago:Abstraction100002137 yago:Act100030358 yago:Activity100407535 yago:Algorithm105847438 yago:Change107296428 yago:Event100029378 yago:Happening107283608 yago:Procedure101023820 yago:PsychologicalFeature100023100 yago:YagoPermanentlyLocatedEntity yago:Rule105846932 yago:Substitution107443761 yago:Variation107337390 yago:WikicatFFTAlgorithms yago:WikicatPermutations
rdfs:label	Bit-reversal permutation (en) Ordenação bit-reversa (pt)
rdfs:comment	Em matemática aplicada, uma ordenação bit-reversa ou uma permutação bit-reversa é uma permutação de uma seqüência de n itens, onde n = 2k é uma potência de dois. Ele é definido pela indexação de elementos da sequência, os números de 0 a n − 1 e, em seguida, invertendo as representações binárias de cada um desses números (acolchoado para que cada um destes números binários tenha comprimento de exatamente k). Cada item é mapeado para a nova posição dada por este valor invertido. O bit de reversão de permutação é uma involução, então repetindo a mesma permutação duas vezes retorna-se para a ordenação original sobre os itens. (pt) In applied mathematics, a bit-reversal permutation is a permutation of a sequence of items, where is a power of two. It is defined by indexing the elements of the sequence by the numbers from to , representing each of these numbers by its binary representation (padded to have length exactly ), and mapping each item to the item whose representation has the same bits in the reversed order. Repeating the same permutation twice returns to the original ordering on the items, so the bit reversal permutation is an involution. (en)
foaf:depiction
dct:subject	Permutations Combinatorial algorithms FFT algorithms
Wikipage page ID	25692725 (xsd:integer)
Wikipage revision ID	1120557118 (xsd:integer)
Link from a Wikipage to another Wikipage	Power of two Binary search tree Permutation Permutations Low-discrepancy sequence Cooley–Tukey FFT algorithm Linear time Lower bound Van der Corput sequence Combinatorial algorithms Data structures Fast Fourier transform Radix Involution (mathematics) Kaczmarz method FFT algorithms Mixed radix In-place algorithm Random-access machine Sequence Memory hierarchy Unit interval Fixed-point arithmetic Vectored I/O Dyadic rational number In-place Binary representation Splay trees
sameAs	Bit-reversal permutation Bit-reversal permutation Bit-reversal permutation Bit-reversal permutation Bit-reversal permutation Bit-reversal permutation
dbp:wikiPageUsesTemplate	dbt:Not_a_typo dbt:Short_description
thumbnail	wiki-commons:Special:FilePath/Hammersley_set_2D.svg?width=300
has abstract	In applied mathematics, a bit-reversal permutation is a permutation of a sequence of items, where is a power of two. It is defined by indexing the elements of the sequence by the numbers from to , representing each of these numbers by its binary representation (padded to have length exactly ), and mapping each item to the item whose representation has the same bits in the reversed order. Repeating the same permutation twice returns to the original ordering on the items, so the bit reversal permutation is an involution. This permutation can be applied to any sequence in linear time while performing only simple index calculations. It has applications in the generation of low-discrepancy sequences and in the evaluation of fast Fourier transforms. (en) Em matemática aplicada, uma ordenação bit-reversa ou uma permutação bit-reversa é uma permutação de uma seqüência de n itens, onde n = 2k é uma potência de dois. Ele é definido pela indexação de elementos da sequência, os números de 0 a n − 1 e, em seguida, invertendo as representações binárias de cada um desses números (acolchoado para que cada um destes números binários tenha comprimento de exatamente k). Cada item é mapeado para a nova posição dada por este valor invertido. O bit de reversão de permutação é uma involução, então repetindo a mesma permutação duas vezes retorna-se para a ordenação original sobre os itens. (pt)
gold:hypernym	Permutation
prov:wasDerivedFrom	wikipedia-en:Bit-reversal_permutation?oldid=1120557118&ns=0
page length (characters) of wiki page	11992 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Bit-reversal_permutation
is Link from a Wikipage to another Wikipage of	Calkin–Wilf tree List of numerical analysis topics List of permutation topics Organizationally unique identifier Cooley–Tukey FFT algorithm Van der Corput sequence Walsh matrix Stern–Brocot tree Bit-reversal Bit-reversed order Bit reversal Digit-reversal permutation
is Wikipage redirect of	Bit-reversal Bit-reversed order Bit reversal Digit-reversal permutation
is foaf:primaryTopic of	wikipedia-en:Bit-reversal_permutation

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